MinT - Best Known (89−46, 89, s)-Nets in Base 16

Best Known (89−46, 89, s)-Nets in Base 16

(89−46, 89, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 89, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 89, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(89−46, 89, 276)-Net over F₁₆ — Digital

Digital (43, 89, 276)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−46, 89, 28681)-Net in Base 16 — Upper bound on s

There is no (43, 89, 28682)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 146887 508683 684413 354589 556152 775080 887859 262236 680067 974046 718352 530806 011277 271313 020202 893389 729719 970816 > 16⁸⁹ [i]